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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>For a linear first order ODE, <span class="process-math">\(f(x, y)\)</span> need be a linear function of <span class="process-math">\(y\text{,}\)</span> say</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq2_2.html">
\begin{equation}
f(x, y)=-p(x)y+q(x).\tag{2.1.1}
\end{equation}
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<p class="continuation">Then, one has</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq2_2.html">
\begin{equation}
\frac{\textrm{d} y}{\textrm{d} x}+p(x) y=q(x).\tag{2.1.2}
\end{equation}
</div>
<p class="continuation">Equation (<a href="" class="xref" data-knowl="./knowl/eq2_2.html" title="Equation 2.1.2">(2.1.2)</a>) is the first order linear ODE.</p>
<span class="incontext"><a href="sec2_1.html#p-16" class="internal">in-context</a></span>
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